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Causal Inference under Interference through Designed Markets

Evan Munro

Abstract

In auction and matching markets, estimating the welfare effects of demand-side treatments is challenging because of spillovers through the mechanism. We develop a quasi-experimental approach that avoids parametric assumptions typically imposed by structural methods. For a class of strategy-proof "cutoff" mechanisms, we propose an estimator that runs a weighted and perturbed version of the mechanism on data from a single market. The estimator is semi-parametrically efficient, asymptotically normal, and robust to a wide class of demand-side specifications. We propose spillover-aware targeting rules with vanishing asymptotic regret. Empirically, spillovers diminish the effect of information on inequality in Chilean schools.

Causal Inference under Interference through Designed Markets

Abstract

In auction and matching markets, estimating the welfare effects of demand-side treatments is challenging because of spillovers through the mechanism. We develop a quasi-experimental approach that avoids parametric assumptions typically imposed by structural methods. For a class of strategy-proof "cutoff" mechanisms, we propose an estimator that runs a weighted and perturbed version of the mechanism on data from a single market. The estimator is semi-parametrically efficient, asymptotically normal, and robust to a wide class of demand-side specifications. We propose spillover-aware targeting rules with vanishing asymptotic regret. Empirically, spillovers diminish the effect of information on inequality in Chilean schools.

Paper Structure

This paper contains 28 sections, 21 theorems, 125 equations, 3 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Defining Counterfactuals
  4. Estimating Counterfactual Values
  5. Policy Learning
  6. Unconstrained Class of Treatment Rules
  7. Constrained Class of Treatment Rules
  8. Simulation
  9. Impact Evaluation in the Chilean School Market
  10. Treatment Effect Estimates
  11. Discussion
  12. Proofs of Main Results
  13. Notation
  14. Proof of Theorem \ref{['thm:moment']}
  15. Proof of Theorem \ref{['thm:norm']} and Corollary \ref{['cor:norm']}
  16. ...and 13 more sections

Key Result

Theorem 1

Under Assumption as:id- as:regulare, $\bar{\tau}_{\text{GTE}}$ has the following asymptotically linear form: where $q_{w} (b, x, p) = y(b, x, p) - \nu^*_w (d(b,x, p) - s^*)$ and $\nu^*_w = \nabla_p^{\top}\mathbb E [ y(B_i(w), X_i, p^*_w) ] ( \nabla_p \mathbb E[d(B_i(w), X_i, p^*_w)])^{-1}.$

Figures (3)

  • Figure 1: The DR-ATE estimator of the direct effect over-estimates the access of treated families to good-quality schools and under-estimates the access of control families.
  • Figure 2: The estimated percentage of low-income families assigned to a good-quality school for different treatment rules. Error bars are standard errors
  • Figure 3: Monte Carlo Simulation Results

Theorems & Definitions (39)

  • Example 1
  • Example 2
  • Definition 1
  • Theorem 1
  • Definition 2
  • Theorem 2
  • Corollary 3
  • Theorem 4
  • Proposition 5
  • Theorem 6
  • ...and 29 more